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Volume of a Room - Math 126

by evone
(jacksonville)










































Choose a room in your house. Measure the length, the width, and the height. Make sure you use feet and inches. Most rooms are not a whole number, such as 10 feet; they are 10 feet and 3 inches, or 9 feet 6 inches, etc.
NOTE: Do not use decimal numbers for the feet. For example, do not write 10.3 to mean 10’3”, because that is incorrect. Convert the measurements to all inches for step 2, and then convert back to square feet for step 3.
Record your dimensions and, using the appropriate formula, find the surface area of the room.
A gallon of paint covers about 350 square feet. How many gallons would be required to paint the room? Round up to the nearest gallon.
If a gallon of paint costs $22.95 plus 8% tax, what would be the total cost to paint the room?
One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions.
Find the volume in cubic centimeters. Be neat and precise.
If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Show your work.

this is the equation 2(8((10)+8(9.5)+10(9.5)= What is the answer, please I have tried everything.

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Apr 18, 2012
Volume of a Room – Cost of Painting
by: Staff

Part I

Question:

by Evone
(Jacksonville)


Choose a room in your house. Measure the length, the width, and the height. Make sure you use feet and inches. Most rooms are not a whole number, such as 10 feet; they are 10 feet and 3 inches, or 9 feet 6 inches, etc.

NOTE: Do not use decimal numbers for the feet. For example, do not write 10.3 to mean 10’3”, because that is incorrect. Convert the measurements to all inches for step 2, and then convert back to square feet for step 3.

Record your dimensions and, using the appropriate formula, find the surface area of the room.
A gallon of paint covers about 350 square feet. How many gallons would be required to paint the room? Round up to the nearest gallon.

If a gallon of paint costs $22.95 plus 8% tax, what would be the total cost to paint the room?
One inch is equivalent to 2.54 centimeters. Convert your English measurements to metrics. Record each dimension in centimeters. Show your conversions.

Find the volume in cubic centimeters. Be neat and precise.

If each dimension (length, width, and height) is doubled, what happens to the volume of the room? Show your work.

this is the equation 2(8((10)+8(9.5)+10(9.5)= What is the answer, please I have tried everything.


Answer:


Measure the length, the width, and the height of a room.

(Hi Evone. These are the measurements I got from your equation. If the values are not correct, you can easily replace them with the correct values. The procedure for calculating the answers to the questions in the problem statement will be the same, regardless of the numbers.)

Length: 9 ft 6 in

Width: 10 ft exactly

Height: 9 ft 6 in


Convert the measurements to all inches

(1 foot = 12 inches. )

Length:

9 ft + 6 in
= 9 ft * 12 in/ft + 6 in
= 108 in + 6 in
= 114 in

Width: 10 ft exactly

10 ft * 12 in/ft
= 120 in

Height: 9 ft 6 in

9 ft + 6 in
= 9 ft * 12 in/ft + 6 in
= 108 in + 6 in
= 114 in


Compute the Surface Area of the Room in square feet

Surface area of 1 wall = width * height

Calculations make no allowances for windows or doors.

Calculations do include the floor.

1st two opposite walls = 2 * (114 in) * (114 in) = 25992 in²

2nd two opposite walls = 2 * (120 in) * (114 in) = 27360 in²

Ceiling = (114 in) * (120 in) = 13680 in²

Floor = (114 in) * (120 in) = 13680 in²


Total surface area of the room

= 25992 in² + 27360 in² + 13680 in² + 13680 in²
= 80712 in²

-------------------------------------------------------------------

Apr 18, 2012
Volume of a Room – Cost of Painting
by: Staff

-------------------------------------------------------------------

Part II

Total surface area of the room in square feet

= 80712 in² * 1 ft²/144 in²

= (80712/144) * ft² * (in²/ in²)

(notice that the units in²/in² cancel one another in the same way two numbers which are equal would cancel one another)

= (80712/144) * ft² * (1)

= (80712/144) * ft²

= 560.5 ft²

How many gallons would be required to paint the room?

Painting the room generally does not include the floor. However, the prior question asked for the total surface area of the entire room. I am going to leave the surface area of the floor in the calculations.

Gallons of paint = (Total surface area in ft²) * (1 gallon)/( ft² covered)

= (560.5ft²) * (1 gallon/350 ft²)

= (560.5 / 350) * (1 gallon) * (ft²/ft²)

= (560.5 / 350) * (1 gallon) * (1)

= (560.5 / 350) * (1 gallon)

= 1.60143 gallons

Rounding up (you must buy 2 gallons of paint, not 1.60 gallons)

= 2 gallons


total cost to paint the room

Cost of Paint = (number of gallons)(cost per gallon) + (sales tax)

Cost of Paint = (2 gallons)*( $22.95/gallon) + (2 gallons)*( $22.95/gallon) (.08)

Cost of Paint = 2*$22.95*(gallons/gallons) + 2*$22.95*(gallons/gallons)*(.08)

Cost of Paint = 2*$22.95*(1) + 2*$22.95*(1)*(.08)

Cost of Paint = 2*$22.95 + 2*$22.95*(.08)

Cost of Paint = $45.90 + $45.90*(.08)

Cost of Paint = $45.90 + $3.67

Cost of Paint = $49.57



Convert your English measurements to metrics


Length: = (114 in)*(2.54 cm/in) = 289.56 cm

Width: = (120 in)*(2.54 cm/in) = 304.80 cm


Height: = (114 in)*(2.54 cm/in) = 289.56 cm


Find the volume in cubic centimeters.

Volume = length * width * height

= (289.56 cm) * (304.80 cm) * (289.56 cm)

= 25,555,954.04928 cm³



If each dimension (length, width, and height) is doubled, what happens to the volume of the room?

Volume1 = length * width * height

Volume2 = 2*length * 2*width * 2*height

Divide Volume2 by Volume1

Volume2/Volume1 = (2*length * 2*width * 2*height)/(length * width * height)

Volume2/Volume1 = (2*length/length) * (2*width/width) * (2*height/height)

Volume2/Volume1 = (2*1) * (2*1) * (2*1)

Volume2/Volume1 = 2 * 2 * 2

Volume2/Volume1 = 8

If every dimension doubles, the new volume is 8 times the original volume.


Thanks for writing.

Staff
www.solving-math-problems.com


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